Work done by a variable force question

  • #1

Homework Statement



246kgu9.jpg


That's a graph of Force in newtons (y axis) vs displacement in meters (x axis) for an object of mass 3.0kg that is moving along the x-axis and initially starts at rest. I am being asked to find the total work done on the object as it moves from x = 0 to x = 7.


Homework Equations



Net Work = ∫F dx = ΔK
K = 1/2mv^2

The Attempt at a Solution



So, I integrated the function and ended up with a total work of -.5J. What I want to know is if this violates the work-energy theorem or not. If the net work is equal to change in kinetic energy, and the object starts at rest, this would mean that -.5 = 1/2mv^2. Is there something really obvious that I'm missing here?
 

Answers and Replies

  • #2
1,506
18
work done (energy) = area under F against x graph (this is another way of seeing ΔK = ∫F.dx
There are 2 clear areas to calculate..... when F is +ve and when F is -ve
 
  • #3
1,506
18
By calculating the areas I got total work = -0.5J
 
  • #4
So, I integrated the function and ended up with a total work of -.5J. What I want to know is if this violates the work-energy theorem or not. If the net work is equal to change in kinetic energy, and the object starts at rest, this would mean that -.5 = 1/2mv^2. Is there something really obvious that I'm missing here?
Can you explain why you think the work-energy theorem is violated?

[itex]0.5=\frac{1}{2}mv^{2}_{f}-\frac{1}{2}mv^{2}_{i}[/itex]

If the object started at rest, the last term is 0 and you get

[itex]0.5=\frac{1}{2}mv^{2}_{f}[/itex]

which just says that the object has some final velocity.
 
  • #5
Can you explain why you think the work-energy theorem is violated?

[itex]0.5=\frac{1}{2}mv^{2}_{f}-\frac{1}{2}mv^{2}_{i}[/itex]

If the object started at rest, the last term is 0 and you get

[itex]0.5=\frac{1}{2}mv^{2}_{f}[/itex]

which just says that the object has some final velocity.
Right, but if the total work done is -.5, wouldn't that mean that
[itex]-0.5=\frac{1}{2}mv^{2}_{f}[/itex]
I'm not sure why you ignored the sign on the work done.
 

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